where \(\mathbf {h}_\mathrm {f} \in \mathbb {C}^N\)  is the fault-induced channel deviation.
Due to the failure pattern sparsity that usually only a small number of antenna elements are faulty [1]}, [2]}, \(\mathbf {h}_\mathrm {f}\)  is assumed as a sparse vector, in which non-zero entries indicate faulty antenna elements.
